One important issue in understanding and modeling of turbulent heat transfer is the behavior of fluctuating temperature close to the wall. Common engineering computational approach assumes constant heat flux boundary condition on heated walls. In the present paper constant heat flux boundary condition was assumed and effects of temperature fluctuations are investigated using large eddy simulations (LES) approach. A series of large eddy simulations for two geometries is performed: First, forced convection in channels and second, forced convection over a backward facing step. LES simulation data is statistically analyzed and compared with results of direct numerical simulations (DNS) from the literature which apply three cases of heat flux boundary conditions: 1. ideal heat flux boundary condition, 2. non-ideal heat flux boundary condition, 3. conjugate heat transfer boundary condition. For low Prandtl number flows LES results show that, despite very good agreement for velocities and mean temperature, predictions of temperature fluctuations may have strong deficiencies if simplified boundary conditions are applied.

The Fluoride-salt-cooled High temperature Reactors (FHRs) are an advanced concept using a novel combination of high-temperature coated-particle fuel, low-pressure fluoride-salt coolant and air-Brayton power conversion system. Prismatic fuel or pebble fuel are adopted for the conceptual core designs of FHRs like TMSR-SF, MK1 PB-FHR and SM-AHTR. The high-Prandtl-number FLiBe is mainly adopted as the primary coolant, which specifies in high melting and boiling point and high volumetric capacity. The experimental results obtained from the air, water or inert gas prove reliable for the Prandtl number vary from 0.7 to 7. Little experimental research has been conducted to prove applicability of the above results to the high-Prandtl fluid, fluoride salts in the packed pebble bed. In this paper, a pebble bed experimental facility has been designed and constructed for the FHRs to explore the thermal-hydraulic characteristics of fluoride salts in the reactor pebble bed core. Dowtherm A is adopted as a simulant fluid for the fluoride salts. The cylindrical test section is packed with steel pebbles. The electromagnetic induction heating system is used to provide internal heat source for the pebble beds. The forced flow and convective heat transfer of high-Prandtl-number fluid in the pebble bed with internal heat generation are investigated in the experiment. The fluid inlet temperature and mass flow rate are studied on the thermal-hydraulic characteristics.

In this paper, a simplified force-balance model in horizontal flow boiling is proposed by introducing several dominant dimensionless parameters. Forces acting on a bubble attached in the direction parallel to the heating surface are analyzed completely, which include quasi-steady drag force, surface tension force and growth force in x-direction. When the force balance is broken in the x-direction before the y-direction, bubble will departure from the nucleation site immediately. Based on the force-balance analysis, bubble departure diameter is formulated to be a function of Jakob number, Reynolds number and Prandtl number. By analyzing the effects of dimensionless parameters, it is found higher Jakob number indicates larger bubble departure diameter, while the increase of Reynolds number will reduce the departure diameter. Besides, the simplified model is able to enlarge application of force-balance model under various dimensionless parameters and make the calculation of bubble departure diameter much easier. Finally, comparing with the experimental data reported in literature, the error between simplified force-balance model and experimental is about 25%.

A detailed safety assessment of innovative Generation IV reactor designs with heavy-liquid metal coolants, such as lead and lead-bismuth eutectic (LBE), requires an evaluation of the maximum core temperature in several postulated scenarios. Considering the complex geometry of fuel assemblies (FAs), and the low Prandtl number of the coolants, this flow scenario is challenging for the models used in numerical simulations, e.g. for relating the turbulent transport of momentum and heat. Thus, reliable experimental data are needed for validation. In recent years, a series of comprehensive heat transfer tests in fuel pin bundle simulators was performed at ENEA (Italy) and KIT (Germany) in the framework of the European collaborative projects THINS and SEARCH. Both grid and wire spacer geometries are considered, in a wide range of operating conditions (temperature, flow velocity and power density) representative of the ALFRED and MYRRHA fuel assemblies, in natural and forced-convective flow regimes. Although different experimental approaches were followed by each group (e.g. thermocouple position and average data treatment), there is a relatively good agreement on results in the overlapping regions. These experimental studies indicate that the mean Nusselt number is in well agreement with the predictions of empirical correlations developed for sodium systems. In particular, for wire-spaced FA, heat transfer results show values close to the Kazimi-Carelli correlation both for low and high flow rates at ENEA and KIT respectively. For grid-spaced FA, results are more in agreement with Ushakov correlation. Furthermore, large temperature differences are measured by thermo-couples installed at selected rods and sub-channels. A discussion on the influences of the spacer design and bundle size is included. This wide comparison allows an overview of the research on the HLM cooled fuel assembly in Europe.

Computational Fluid Dynamics (CFD) is a numerical approach to modelling fluids in multidimensional space using the Navier-Stokes equations and databases of fluid properties to arrive at a full simulation of a fluid dynamics and heat transfer system. The turbulence models employed in CFD are a set of equations that determine the turbulence transport terms in the mean flow equations. They are based on hypotheses about the process of turbulence, and as such require empirical input in the form of constants or functions, in order to achieve closure. By introducing a set of empirical constants to a model, that model then becomes valid for certain flow conditions, or for a range of flows. Of those constants, the turbulent Prandtl number appears in multiple equations; energy, momentum, turbulent kinetic energy, turbulent kinetic energy dissipation rate, etc. and the value it takes in each equation is different and chosen empirically to fit a wide range of flows in the subcritical region. The studies that attempt to find the effect of varying the turbulent Pr number on simulation results, often only mention one number; presumably the one that appears in the energy equation (although it is never explicitly explained). The rest of the constants are treated as universally acceptable for generalized flow and not tested for their effect on flow parameters. A numerical study on heat transfer to supercritical water flowing in a vertical tube is carried out using the ANSYS FLUENT code and employing the Realizable k-ε (RKE) and the SST k-ε turbulence models. The 3-D mesh consists of a 1/8 slice (45° radially) of a bare tube. The study explored the effects of turbulent Pr numbers, and their variations, in order to understand their significance, and to build on previous knowledge to modify the turbulence models and achieve higher accuracy in simulating experimental conditions. The numerical results of 3D flow and thermal distributions under normal and deteriorated heat transfer conditions are compared to experimental results. The distributions of temperature and turbulence levels are used to understand the underlying phenomena of the heat transfer deterioration in supercritical water flows. Reducing the energy turbulent Pr number produced the most accurate prediction of the deterioration in heat transfer, by altering the production term due to buoyancy, which appears in the equations for turbulent kinetic energy as well as its dissipation rate. The buoyancy forces in upward flows act to reduce the turbulent shear stress, resulting in localized increase in wall temperatures.

The purpose of the present research was to explore the role of rectangular roughness elements during natural convection in a two-dimensional rectangular cavity. The computational algorithm was developed based on the single relaxation time Bhatnagr-Gross and Krook (BGK) model of lattice Boltzmann method (LBM). Rectangular roughness elements were located on the horizontal walls. The computational algorithm was validated against benchmark studies using different numerical techniques, and a good agreement was found to exist. The range of the Rayleigh (Ra) number was explored from 10 3 to 10 6 for a Newtonian fluid of Prandtl number equal to 1.0. The dimensionless amplitude (h/H) of roughness elements was fixed to 0.1, while the spacing between these elements was equal to twice their height. The maximum reduction in the average heat transfer was calculated to be 27 percent at Ra number 1×10 6 .

Mixed convection heat transfer in heated tubes has been studied extensively in the past decades, which is widely used in various industrial fields such as cooling of a nuclear reactor core. The secondary flow, which is induced by buoyancy force, has been found in previous research to have profound influence on the heat transfer difference on circumferential position and occurrence of heat transfer deterioration in horizontal heated channel. Therefore, understanding the secondary flow velocity field has important implications to prevent heat transfer deterioration and ensure the safe operation of nuclear power plants. Numerical methods have been adopted in literature to analyze the complex interaction between secondary flow and heat transfer deterioration. However, to the knowledge of the author, experimental measurement of secondary flow in the radial cross-section of a horizontal tube does not exist. In this paper, a novel measurement method, which combines the transparent heating and PIV (Particle Image Velocimetry) technology, has been adopted to experimentally investigate the secondary flow velocity field on the radial cross-section in a horizontal heated tube. The heat transfer deterioration mechanism is revealed through analysis of the distribution of secondary flow along circumference direction at low mass flow rates and high heat flux conditions. We found that the buoyancy force lead the hot fluid to rise along the tube wall from bottom to top. While the secondary flow is most intensive near the middle of the interface, the secondary velocities are high at the bottom of the cross-section, where the tube wall is well cooled by cold fluid descends from the central part of the cross-section. Near the top of the tube wall, the secondary velocities are very small and the thermal acceleration effect makes the fluid rise. As a result, the mixed convection of top and center part of cross-section is weak and heat is primarily transferred by conduction, which leads the occurrence of thermal stratification of fluid. Consequently, the thermal accumulation of fluid in the top leads to heat transfer deterioration. Moreover, thermal properties differences between Freon (FC-72) and water, especially the Prandtl number (Pr), make the occurrence of heat transfer deterioration much easier for FC-72 than water with same working conditions.

In this study, validations of Reynolds Averaged Navier-Stokes Simulation (RANS) based on Kenjeres & Hanjalic MHD turbulence model (Int. J. Heat & Fluid Flow, 21, 2000) coupled with the low-Reynolds number k-epsilon model have been conducted with the usage of Direct Numerical Simulation (DNS) database. DNS database of turbulent channel flow imposed wall-normal magnetic field on, are established in condition of bulk Reynolds number 40000, Hartmann number 24, and Prandtl number 5. As the results, the Nagano & Shimada model (Trans. JSME series B. 59, 1993) coupled with Kenjeres & Hanjalic MHD turbulence model has the better availability compared with Myong & Kasagi model (Int. Fluid Eng, 109, 1990) in estimation of the heat transfer degradation in MHD turbulent heat transfer.

In this study, validations of Reynolds Averaged Navier-Stokes Simulation (RANS) based on Kenjeres & Hanjalic MHD turbulence model (Int. J. Heat & Fluid Flow, 21, 2000) coupled with the low-Reynolds number k-epsilon model have been conducted with the usage of Direct Numerical Simulation (DNS) database. DNS database of turbulent channel flow imposed wall-normal magnetic field on, are established in condition of bulk Reynolds number 40000, Hartmann number 24, and Prandtl number 5. As the results, the Nagano & Shimada model (Trans. JSME series B. 59, 1993) coupled with Kenjeres & Hanjalic MHD turbulence model has the better availability compared with Myong & Kasagi model (Int. Fluid Eng, 109, 1990) in estimation of the heat transfer degradation in MHD turbulent heat transfer.

This work presents an analysis of the turbulent natural convection in a volumetrically hemisphere cavity, representing a lower plenum of a Light Water Reactor (LWR) vessel. Considering isothermal top and bottom walls at temperature of 298.5 K and a fluid with Prandtl number (Pr) equal to 8.52 , the experiment performed by Asfia et al. [1] was reproduced, so that their experimental data could be used for the validation of the numerical data provided by the present work. Ranging the internal Rayleigh numbers (Ra i ) from 10 8 to 3.03 × 10 13 , numerical simulations were performed using the open-source Computational Fluid Dynamics (CFD) code OpenFOAM (Open Field Operation and Manipulation), making use of the “code-friendly” modification of the turbulence model V2-f, a Reynolds Averaged Navier-Stokes (RANS) based equation model. The calculation of the turbulent heat fluxes was done by the Simple Gradient Diffusion Hypothesis (SGDH), which proved to be adequate for the case considered. Bearing in mind the complexity of the phenomena inside a molten core after a severe accident in a nuclear power plant, some assumptions were done such as the fluid was considered Newtonian, with no-phase change and homogeneous. Numerical correlations of Nusselt number ( Nu ¯ ) over the bottom and top walls as function of the Ra i were obtained and a good agreement with the experimental data provided by Asfia et al. [1] was reached for the local heat transfer with respect to the angle for the cooled top wall.

This work aimed to analyze the turbulent natural convection in a volumetrically heated fluid with Prandtl number equal to 0.6 , representing the oxide material layer of a corium. Four turbulence models were scrutinized in order to select the most appropriate one for turbulence modeling based on Reynolds Averaged Navier-Stokes equations (RANS) of natural convection in a molten core. The turbulence models scrutinized are the standard k- ε , Shear Stress Transport (SST), low-Reynolds-k- ε (Launder-Sharma) and also an elliptic blending model ν 2 -f. The simulations were carried out in a square cavity with isothermal walls, for Rayleigh numbers (Ra) ranging from 10 9 to 10 11 . The numerical simulations, performed in an open-source of Computational Fluid Dynamics (CFD) - OpenFOAM (Open Field Operation and Manipulation), provided outcomes of average Nusselt number as function of Ra number, which were in a reasonable agreement with an experimental correlation and other authors’ simulations. It was also possible to observe the limitations and robustness of each model analyzed, enabling to conclude that the most adequate turbulence models for the present physical problem were SST and ν 2 -f.

In the frame of the validation and verification of the thermal hydraulic system code TRACE for lead alloy cooled systems, a 19 pin bundle is analyzed, in particular, the influence of the spacers. TRACE is updated and improved in order to be used for the analyses of liquid metal cooled reactors. For the present investigation, isothermal hydraulic experiments, carried out at the Karlsruhe Lead Laboratory, are used to validate the pressure losses related to wall friction and spacers. In this experimental set-up, a 19 rod bundle, cooled by liquid lead-bismuth eutectics (LBE) is used. In addition, thermal analyses are performed in order to evaluate the axial temperature profile of coolant and cladding and to validate the chosen heat transfer models. Since the thermal experiments have not been performed yet, the validation is done by comparing TRACE results to CFD results following a unique approach for the turbulent Prandtl number. Special emphasize is paid to the validation of the models to account for heat transfer enhancement at and in the vicinity of spacers due to increased turbulences.

A pre-test CFD analysis has been performed for the new Fuel bundle experiment to be carried out in the CIRCE facility. For a fixed pitch to diameter ratio of 1.8, fully developed and 3D analysis are presented for the elementary subchannel. The full 3D subchannel with non-active zones and spacer grids is simulated to study the entry effects and the local perturbation induced by the grid. The thermal peaking factor and the pressure loss induced by the central spacer grid is also evaluated. In liquid metals, due to the low Prandtl number, the thermal boundary layer is much larger than the mechanical one, and therefore the bulk temperature does not coincide with the central channel temperature. On the basis of computational results, the ‘correct’ heat transfer coefficient based on wall temperature and bulk temperature is compared with the practical experimental measurement evaluation based on wall-thermocouples and central channel temperature. Moreover, The realistic non-uniform heat flux of the pins is taken into account in order to evaluate the local variation of heat transfer coefficient and temperature due to this effect.

The paper reports computational simulation of natural convection of a molten core during a hypothetical severe accident in the lower head of a typical PWR pressure vessel. Numerical simulations were carried out for a two-dimensional semi-circular slice geometry which represents the lower head of a PWR pressure vessel. Transient turbulent natural convection heat transfer of a fluid with uniformly distributed volumetric heat generation rate is simulated by using a commercial computational fluid dynamics (CFD) software ANSYS CFX 12.0. The bottom circular surface and top flat surface are both kept at a same constant temperature. The Boussinesq model is used for the buoyancy effect generated by the internal heat source in the flow field. The two-equation k-ω based SST (shear stress transport) turbulent model is used to model the turbulent eddy viscosity. Two Prandtl numbers are considered, 6.13 and 7.0 . Five Rayleigh numbers were simulated for each Prandtl number: 10 9 , 10 10 , 10 11 , 10 12 , and 10 13 . The average Nusselt numbers on the bottom surface calculated by the computational simulations are in excellent agreement with Mayinger et al. (1976) correlation, with the average Nusselt number on the top flat surface calculated by the computational simulation is in excellent agreement with Mayinger et al. (1976) and Kulacki and Emara (1975) correlations only at Ra = 10 9 . Numerical results of the velocity and temperature fields show the α-phenomena at lower Rayleigh number and ν -phenomena at lower Rayleigh number.

In the framework of accelerator driven sub-critical reactor systems (ADS), heavy liquid metals (HLM), in particular lead or lead bismuth eutectic (LBE), are considered as coolant for the reactor core and the spallation target due to their efficient heat removal properties and high production rate of neutrons. LBE-flows are characterized by excellent heat conductivity and exhibit a low molecular Prandtl number of the order 10 −2 leading to distinct thermal and viscous boundary layers and scale separation in both the time and spatial domain. Since the analogy of turbulent heat and momentum transfer is employed in common turbulence models but is not valid in HLM flows, commercially available fluid dynamic code systems cannot predict heat transfer adequately for such flows. In order to provide validation data and heat transfer correlations, a series of three major experiments has been launched at the KArlsruhe Liquid metal LAboratory (KALLA) of the Karlsruhe Institute of Technology and will be presented in this overview.

The flowing and heat transfer characteristics of turbulent flow in tubes in rolling motion are investigated theoretically. The flowing and heat transfer models of turbulent flow in rolling motion are established. The correlations of frictional resistance coefficient and Nusselt number are derived. The results are also validated with experiments. The effects of several parameters on Nusselt number are investigated. The oscillating amplitude of Nusselt number is in direct ratio with Prandtl number and rolling frequency approximately. The more the flowing velocity is, the less the effect of rolling motion on the flow is. The variation of initial phase difference between Nusselt number and rolling motion with rolling frequency is very limited.

This paper presents selected results on heat transfer to supercritical water flowing upward in a 4-m-long vertical bare tube. Supercritical water heat-transfer data were obtained at pressures of about 24 MPa, mass fluxes of 200 – 1500 kg/m 2 s, heat fluxes up to 884 kW/m 2 and inlet temperatures from 320 to 350°C for several combinations of wall and bulk-fluid temperatures that were below, at or above the pseudocritical temperature. In general, the experiments confirmed that there are three heat-transfer regimes for forced convective heat transfer to water flowing inside tubes at supercritical pressures: (1) normal heat-transfer regime characterized in general with heat transfer coefficients (HTCs) similar to those of subcritical convective heat transfer far from critical or pseudocritical regions, which are calculated according to the Dittus-Boelter type correlations; (2) deteriorated heat-transfer regime with lower values of the HTC and hence higher values of wall temperature within some part of a test section compared to those of the normal heat-transfer regime; and (3) improved heat-transfer regime with higher values of the HTC and hence lower values of wall temperature within some part of a test section compared to those of normal heat-transfer regime. These new heat-transfer data are applicable as a reference dataset for future comparison with supercritical-water bundle data and for a verification of scaling parameters between water and modeling fluids. Also, these HTC data were compared to those calculated with the original Dittus-Boelter and Bishop et al. correlations. The comparison showed that the Bishop et al. correlation, which uses the cross-section average Prandtl number, represents HTC profiles more correctly along the heated length of the tube than the Dittus-Boelter correlation. In general, the Bishop et al. correlation shows a good agreement with the experimental HTCs outside the pseudocritical region, however, overpredicts the experimental HTCs within the pseudocritical region. The Dittus-Boelter correlation can also predict the experimental HTCs outside the pseudocritical region, but deviates significantly from the experimental data within the pseudocritical region. It should be noted that both these correlations cannot be used for a prediction of HTCs within the deteriorated heat-transfer regime.

The use of accurate heat transfer model in liquid metal like Lead Bismuth Eutectic (LBE) flow is essential for the designing of the liquid metal cooled nuclear reactor systems. In the present study, the existing physical correlations for heat transfer in LBE flow through circular tube have been reviewed and assessed with the experimental results. In CFD analysis, PHOENICS-3.6 is used to carry out the evaluation of the various turbulence models in the tube geometry and to identify the difference between the numerical results and experimental ones in LBE flows. Based on the assessment of the existing correlations for heat transfer in LBE flow and the CFD results achieved, the best-suited correlation for turbulent Prandtl number is recommended in terms of Peclet number. This Pr t can be incorporated in PHOENICS for LBE flow analysis.

In the last phase of the core degradation, an oxidic melt pool of mainly UO 2 , ZrO 2 , and unoxidized Zircaloy and stain-less steel will form in the lower head of the RPV (Theofanous et al., 1996). A molten metal layer (composed mainly of Fe and Zr ) will rest on the top of the crust of the oxidic pool. A thin oxidic crust layer of frozen core material is formed on the vessel’s inside wall. In this bounding configuration, thermal loads to the RPV walls are determined by natural convection heat transfer driven by internal heat sources. Decay heat from fission products is assumed to be generated uniformly within the oxidic pool and generally no heat generation is considered in the upper metallic layer. For example, in a hypothetical severe accident scenario for an AP600-like reactor, the following values can be expected: volumetric heat generation Q v ∼ 1 MW/m 3 , volume of the oxidic pool V ∼ 10 m 3 , radius R = 2 m, temperatures in the oxidic pool T ∼ 2700°C, temperatures in the metal layer T ∼ 2000°C, maximum depth ratio of the metal layer to the oxidic pool L 12 ∼ 0:3, properties of the oxidic pool, depending on melt composition, as characterized by the Prandtl number, Pr ∼ 0:6, properties of the metallic layer Pr < 0:1, the intensity of convective motion, as characterized by the Rayleigh number, Ra ∼ 10 15 –10 16 (Theofanous et al., 1996). The time scale of core melt pool formation is estimated as 1/2 to 1 hour (Sehgal, 1999). Indeed, these estimates could vary, depending very much on the accident scenario and the type of reactor.

An experimental study is performed to investigate the natural convection heat transfer characteristics with subcooled coolant to create engineering database for basic applications in a lead alloy cooled reactor. Tests are performed in the ALTOS (Applied Liquid-metal Thermal Operation Study) apparatus as part of MITHOS (Metal Integrated Thermo Hydrodynamic Operation System). A relationship is determined between the Nusselt number Nu and the Rayleigh number Ra in the liquid metal rectangular pool. Results are compared with correlations and experimental data in the literature. Given the similar Ra condition, the present test results for Nu of the liquid metal pool with top subcooling are found to be similar to those predicted by the existing correlations or experiments. The current test results are utilized to develop natural convection heat transfer correlations applicable to low Prandtl number Pr fluids that are heated from below and cooled by the external coolant above. Results from this study are slated to be used in designing BORIS (Battery Optimized Reactor Integral System), a small lead cooled modular fast reactor for deployment at remote sites cycled with MOBIS (Modular Optimized Brayton Integral System) for electricity generation, tied with NAVIS (Naval Application Vessel Integral System) for ship propulsion, joined with THAIS (Thermochemical Hydrogen Acquisition Integral System) for hydrogen production, and coupled with DORIS (Desalination Optimized Reactor Integral System) for seawater desalination. Tests are performed with Wood’s metal (Pb-Bi-Sn-Cd) filling a rectangular pool whose lower surface is heated and upper surface cooled by forced convection of water. The test section is 20 cm long, 11.3 cm high and 15 cm wide. The simulant has a melting temperature of 78°C. The constant temperature and heat flux condition was realized for the bottom heating once the steady state had been met. The test parameters include the heated bottom surface temperature of the liquid metal pool, the input power to the bottom surface of the section, and the coolant temperature.